Find Length of Longest Subsequence of One String Which is Substring of Another String in C++

Suppose, we have two strings X and Y, and we have to find the length of longest subsequence of string X, which is substring in sequence Y. So if X = “ABCD” and Y = “BACDBDCD”, then output will be 3. As “ACD” is the longest sub-sequence of X, which is substring of Y.

Here we will use the dynamic programming approach to solve this problem. So if the length of X is n, and length of Y is m, then create DP array of order (m+1)x(n+1). Value of DP[i, j] is maximum length of subsequence of X[0…j], which is substring of Y[0…i]. Now for each cell of DP, it will follow like below:

• for i in range 1 to m:
  • for j in range 1 to n
    • when X[i – 1] is same as Y[j – i], then DP[i, j] := 1 + DP[i – 1, j – 1]
    • Otherwise DP[i, j] := 1 + DP[i, j – 1]

And finally the length of longest subsequence of x, which is substring of y is max(DP[i, n]), where 1 <= i <= m.

Example

 Live Demo

#include<iostream>
#define MAX 100
using namespace std;
int maxSubLength(string x, string y) {
   int table[MAX][MAX];
   int n = x.length();
   int m = y.length();
   for (int i = 0; i <= m; i++)
      for (int j = 0; j <= n; j++)
   table[i][j] = 0;
   for (int i = 1; i <= m; i++) {
      for (int j = 1; j <= n; j++) {
         if (x[j - 1] == y[i - 1])
            table[i][j] = 1 + table[i - 1][j - 1];
         else
            table[i][j] = table[i][j - 1];
      }
   }
   int ans = 0;
   for (int i = 1; i <= m; i++)
   ans = max(ans, table[i][n]);
   return ans;
}
int main() {
   string x = "ABCD";
   string y = "BACDBDCD";
   cout << "Length of Maximum subsequence substring is: " << maxSubLength(x, y);
}

Output

Length of Maximum subsequence substring is: 3